Make the snapper: Preheat oven to 400 degrees. Place fish on one side of a 12-by-16-inch piece of parchment. Season cavity with salt and pepper, and arrange lime and 1/2 the garlic. Season outside of fish with salt and pepper. Sprinkle remaining garlic on fish, and drizzle with oil and lime juice.
Fold parchment over fish, and seal by making small, tight overlapping folds along edges and ends. Transfer to a baking sheet, and roast until packet puffs and turns light golden, about 20 minutes. Open fish packet carefully. Fish should be opaque in center; if it is not cooked through, reseal parchment and continue roasting.
Make the vinaigrette: Puree all of the ingredients in a blender until smooth.
Transfer fish to cutting board discarding parchment. Debone if desired, and garnish with cilantro. Serve immediately with vinaigrette on the side.